Once you buy an App it is yours on that iTunes account. It can be loaded on any iOS device you control.
You can sync those Apps to your iPad the same way you can add and manage Apps for your iPhone.
Data transfer may be an issue though. Things like save game data in game Apps don't transfer that way. Think of it like a clean install on a new computer.
Some people are cloning thier data by using the "restore from backup" feature of iTunes to get that data from their iPad 1 to thier iPad 2. I do not know if it works going from an iPhone to iPad.
At the very least you could use iPhone Explorer and Phone Disk to manually move that data. Each App contains it's own documents folder where such data is kept. I have not used Phone Disk myself yet. Anyone got any experience with it?
*edit*
Some iPhone Apps are not Universal, meaning they were only built with the iPhone in mind. These will run on the iPad but at reduce screen size or in 2x mode. Some developers make different versions of their Apps specifically for the iPad, which you would have to buy again. Some make it universal.
iTunes keeps three categories, iPhone(iPod), iPad, iPhone/iPad. For example my copy of Chaos Rings is for the iPhone. I can put it on my iPad and run it in 2x mode (will look like shit). I would have to buy Chaos Rings HD (technically a different app) to have better graphics. I also have Infinity Blade which is universal and will have full iPad Graphics at no cost. I have already bought GarageBand which is iPad only, I cannot use it on my iPhone.
*edit*
Just got my iPad 2. Seems to see my latest iPod Touch 3rd Gen backup and is now restoring from it. It did complain that some of the Apps weren't' compatible and would have data restored... guess I'll find out which. Saves me an ass load of work configuring it